Linear Operators, Part 2 |
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Page 926
... theory of Hermitian operators goes back to the work of Hilbert [ 1 , IV ] . Proofs of this result were also given by F. Riesz [ 20 , 6 ] , and contribu- tions were made by many others . The reader is referred to the encyclo- pedic ...
... theory of Hermitian operators goes back to the work of Hilbert [ 1 , IV ] . Proofs of this result were also given by F. Riesz [ 20 , 6 ] , and contribu- tions were made by many others . The reader is referred to the encyclo- pedic ...
Page 937
... theory , it is possible not only to give a satisfactory foundation for these subjects , but also to develop their principal results , and this we shall attempt to do . The topics discussed are group theory and the Peter - Weyl theorem ...
... theory , it is possible not only to give a satisfactory foundation for these subjects , but also to develop their principal results , and this we shall attempt to do . The topics discussed are group theory and the Peter - Weyl theorem ...
Page 1815
... Theory . D. van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press ...
... Theory . D. van Nostrand , New York , 1950 . Introduction to Hilbert space and the theory of spectral multiplicity . Chelsea , New York , 1951 . Finite dimensional vector spaces . Ann . of Math . Stud . No. 7. Princeton Univ . Press ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero